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Sigma Notation - Quiz 1   Last unanswered question  Question  Next unanswered question

Question 1 lion

Which one of the following is the correct expansion of   sum 5 3k ? k=1
a) sum 5 3k = 3 + 4+ 5. k=1   b) 5 sum 3k = 3+ 4 +5 + 6+ 7. k=1
c) sum 5 3k = 3+ 6 +9 + 12+ 15. k=1   d) sum 5 3k = 3+ 6 +9 + 12+ 15+ 18 +.... k=1

 

Not correct. Choice (a) is false.
Try again, remember sum 5 3k = 3× 1 +3 × 2+ ... k=1 until you get to the number on top.
Not correct. Choice (b) is false.
Try again, remember 5 sum 3k = 3× 1 + 3× 2+ ... k=1 until you get to the number on top.
Your answer is correct.
sum 5k=13k = 3× 1 + 3× 2+ 3× 3 + 3× 4+ 3 × 5 = 3+ 6 + 9+ 12+ 15.
Not correct. Choice (d) is false.
Try again, you must stop after 5 terms.
Question 2 lion

The sum 4 sum 2k k=2 is equal to which of the following?
a) 21 + 22 + 23 + 24.   b) 22 + 24.
c) 22 + 33 + 44.   d) 22 +23 + 24.

 

Not correct. Choice (a) is false.
Try again - note that the summation variable starts at 2.
Not correct. Choice (b) is false.
Try again, you need to replace k with 2 then 3 then 4.
Not correct. Choice (c) is false.
Try again, the 2 needs to stay fixed while the index changes.
Your answer is correct.
Question 3 lion

The sum 1 sum 4 4 xm m=1 is equal to which of the following?
a) 1 1 1 1 4x1 + 4 x2 + 4x3 + 4x4.   b) 1x1 + x2 + x3 + x4. 4
c) 1 1 1 x1 + 2x2 + 3x3 + 4x4.   d) 1 4 (1 + 2+ 3+ 4).

 

Your answer is correct.
4 1 sum x 4 m=1 m =1(x + x + x +x ) 4 1 2 3 4
 =1 1 1 1 4x1 + 4 x2 + 4x3 + 4x4.
Not correct. Choice (b) is false.
Try again, every term in the sum has to be multiplied by 1 4 .
Not correct. Choice (c) is false.
Try again, the term 1 4 is fixed.
Not correct. Choice (d) is false.
Try again, the subscript of x is variable that changes, not the value of x .
Question 4 lion

The sum n sum --j-- j=4 j + 1 is equal to which of the following?
a) 1+ 3 + 5 + ...+ --n--. 2 4 6 n + 1   b) 1 2 3 --n-- 2 + 3 + 4 + ...+ n + 1 .
c) 4 + 5+ 6+ ...+ -n---. 5 6 7 n+ 1   d) 4 5 6 n+ 4 -+ -+ - + ...+ -----. 5 6 7 n+ 5

 

Not correct. Choice (a) is false.
Try again, the summation variable starts at 4 and the numerator and denominator only increase by one for each term.
Not correct. Choice (b) is false.
Try again, the summation variable starts at 4.
Your answer is correct.
The summation variable starts at 4 so the first term is 4 5 and the numerator and denominator increase by one for each term and finish at n -----. n+ 1
Not correct. Choice (d) is false.
Try again, the final term is wrong.
Question 5 lion

Which of the following is the expansion of   sum 4 (Oi - Ei)2 ---Ei----? i=1
a) 2 2 2 2 (O1---E1)-+-(O2--E2)--+-(O3---E3)-+-(O4---E4) . E1 + E2 + E3 + E4
b) 2 ((O1---E1)+-(O2---E2)+-(O3--E3)-+-(O4---E4))-. E1 + E2 + E3 + E4
c) 2 2 2 2 (O1---E1)-+ (O2---E2)-+ (O3---E3)-+ (O4---E4)-. E1 E2 E3 E4
d) ( )2 (O1--E1)-+ (O2--E2)-+ (O3---E3)+ (O4---E4) . E1 E2 E3 E4

 

Not correct. Choice (a) is false.
Try again, you do not have the correct denominator.
Not correct. Choice (b) is false.
Try again, you need to square each term and have a look at the denominator.
Your answer is correct.
Not correct. Choice (d) is false.
Try again, you need to square the numerator in each term, not the whole lot.